Whakaoti i te a^2+8a-4=0

$$a ^ { 2 } + 8 a - 4 = 0$$

Whakaoti mō a

$$a=2\sqrt{5}-4\approx 0.472135955$$

$$a=-2\sqrt{5}-4\approx -8.472135955$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$a^{2}+8a-4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 8 mō b, me -4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-8±\sqrt{8^{2}-4\left(-4\right)}}{2}$$

Pūrua 8.

$$a=\frac{-8±\sqrt{64-4\left(-4\right)}}{2}$$

Whakareatia -4 ki te -4.

$$a=\frac{-8±\sqrt{64+16}}{2}$$

Tāpiri 64 ki te 16.

$$a=\frac{-8±\sqrt{80}}{2}$$

Tuhia te pūtakerua o te 80.

$$a=\frac{-8±4\sqrt{5}}{2}$$

Nā, me whakaoti te whārite a=\frac{-8±4\sqrt{5}}{2} ina he tāpiri te ±. Tāpiri -8 ki te 4\sqrt{5}.

$$a=\frac{4\sqrt{5}-8}{2}$$

Whakawehe -8+4\sqrt{5} ki te 2.

$$a=2\sqrt{5}-4$$

Nā, me whakaoti te whārite a=\frac{-8±4\sqrt{5}}{2} ina he tango te ±. Tango 4\sqrt{5} mai i -8.

$$a=\frac{-4\sqrt{5}-8}{2}$$

Whakawehe -8-4\sqrt{5} ki te 2.

$$a=-2\sqrt{5}-4$$

Kua oti te whārite te whakatau.

$$a=2\sqrt{5}-4 a=-2\sqrt{5}-4$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$a^{2}+8a-4=0$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$a^{2}+8a-4-\left(-4\right)=-\left(-4\right)$$

Mā te tango i te -4 i a ia ake anō ka toe ko te 0.

$$a^{2}+8a=-\left(-4\right)$$

Tango -4 mai i 0.

$$a^{2}+8a=4$$

Whakawehea te 8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 4. Nā, tāpiria te pūrua o te 4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$a^{2}+8a+4^{2}=4+4^{2}$$

Pūrua 4.

$$a^{2}+8a+16=4+16$$

Tāpiri 4 ki te 16.

$$a^{2}+8a+16=20$$

Tauwehea a^{2}+8a+16. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(a+4\right)^{2}=20$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(a+4\right)^{2}}=\sqrt{20}$$

Whakarūnātia.

$$a+4=2\sqrt{5} a+4=-2\sqrt{5}$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$a=2\sqrt{5}-4 a=-2\sqrt{5}-4$$